Download 7.1 Trig Problems - Animated Science

AS Physics
Unit 7.1 Sin, Cos & Tan
If we examine the right-angled triangle more closely we can define various
relationships which, we find scientifically useful in physics.
It is simpler to label any triangle generically as such;
The idea is that the adjacent side is next to the angle, the opposite is just that,
opposite to the angle. The hypotenuse is named after the mathematician who
first used such calculations!
There are three main ratios involved in triangles and thus three functions we
will use throughout this course;
They are in fact simple numerical ratios, which yield a generic function. The
ratio tells us about the angle of the triangle. One of these is;
tan  
opp
adj
The inverse function depicted by a –1 index in front of the ratio gives us the
angle in degrees or radians;
1
 opp 

  tan 
 adj 
NB. this is not the same as 1/x function, and make sure you calculator is in
the right mode deg or rad (not grad)
Mr Powell
AS Physics
We also can find the following two ratios in the same way;
adj
cos 
hyp
sin  
opp
hyp
1
 adj 

  cos 
 hyp 
1
 opp 

 hyp 
  sin 
NB. You can change the angle  to be the other angle in the triangle.
However, this also changes the opp & adjacent.
These formulas can be rearranged in any way you like. However, the part
inside the brackets has to stay together if it is part of a function.
Mr Powell
AS Physics
Problems Sheet 1 Simple Trigonometry
Answer the following problems, write out the question, working and
answer on file paper. Use the following formulae;
a2 = b2 + c2 - 2bc cos A
b2 = a2 + c2 - 2ac cos B
c2 = a2 + b2 - 2ab cos C
a
b
c


SinA SinB SinC
tan = opp/adj
sin = opp/hyp
cos = adj/hyp
1) Find the length of BC.
2) Find the size of angle R.
3) Find the size of angle R.
4) Work out both “” angles in degrees for a right-angled triangle if hyp
= 5, opp = 4, adj = 3?
5) Work out opp if  = 450 and the adj = 7cm?
Mr Powell
AS Physics
6) Work out tan and  if opp = 53.0m, adj = 42.0m?
7) Find the length of YZ.
8) Find x
9) Find y
10) Find Z
Mr Powell
AS Physics
Answers
1) 4.86 cm
2) 31.8°
3) 25.4°
4) cos-1(3/5)
5) tan x adj = opp, tan45 x 7 = 7
6) opp/adj = tan, = 53/42 = 1.26 = 1.3 to 1 d.p angle is 51.6°
7) 4.40cm
8) x2 = 212 + 202
212 + 202 = 841
Find the square root of 841
x = 29
9) y2 = 3.22 + 5.52
3.22 + 5.52 = 40.49
Find the square root of 40.49
y = 6.4
10) z2 = 192 - 162
192 - 162 =105
Find the square root of 105
z = 10.2
Mr Powell